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Finance Calc Kit
Investments

Put Call Parity Calculator

Calculate European call and put option prices, spot price, or strike price using the Put-Call Parity formula with arbitrage checks.

Put-call parity inputs

$
$
$
%
years
$

Call option price (C)

$10.00

Present value of strike PV(K)

$95.12

Left side: C + PV(K)

$105.12

Right side: P + S - PV(Div)

$105.12

Parity check

Parity holds (no-arbitrage)

Put-call parity step-by-step

Discount the strike, solve for the selected variable, then verify both sides of parity.

  1. Discount strike price to present value

    PV(K)=K⋅e−rT=100.00⋅e−0.0500×1.00=95.1229PV(K) = K \cdot e^{-rT} = 100.00 \cdot e^{-0.0500 \times 1.00} = 95.1229

    Continuous compounding discounts the strike with e^(-rT).

  2. Rearrange parity to solve for call

    C=P+S−PV(K)−PV(Div)=5.12+100.00−95.1229−0.00=9.9971C = P + S - PV(K) - PV(Div) = 5.12 + 100.00 - 95.1229 - 0.00 = 9.9971

    Put-call parity links call, put, stock, and discounted strike in a no-arbitrage identity.

  3. Verify both sides of put-call parity

    C+PV(K)=10.00+95.1229=105.1200,P+S−PV(Div)=5.12+100.00−0.00=105.1200C + PV(K) = 10.00 + 95.1229 = 105.1200, \quad P + S - PV(Div) = 5.12 + 100.00 - 0.00 = 105.1200

    When parity holds, the left and right sides are equal and no risk-free arbitrage exists.

Report tool

What is put-call parity?

Put-call parity is a no-arbitrage relationship between European call and put options on the same underlying stock, strike, and expiration. If parity fails after adjusting for dividends and interest, a theoretical risk-free profit may exist by combining the option and stock legs.

Once you verify parity, explore multi-leg structures with the options spread calculator to compare defined-risk strategies built from calls and puts.

Put-call parity formula

For European options with present value of dividends PV(Div) and discounted strike PV(K):

C+PV(K)=P+S−PV(Div)C + PV(K) = P + S - PV(Div)

Continuous compounding discounts the strike as K e^(-rT). Discrete compounding uses K / (1 + r)^T. Rearrange the identity to solve for any one of call, put, stock, or strike.

Worked example: solve for the call price

With S = $100, K = $100, P = $5.12, r = 5%, T = 1 year, continuous compounding, and no dividends:

PV(K)=100×e−0.05×1=95.12PV(K) = 100 \times e^{-0.05 \times 1} = 95.12
C=P+S−PV(K)=5.12+100−95.12=10.00C = P + S - PV(K) = 5.12 + 100 - 95.12 = 10.00

Both sides equal $105.12, confirming parity. Switch the solve target to put, stock, or strike to recover the other variables from the same inputs.

Practical notes for traders and students

  • Parity applies to European-style options. American early exercise can break the simple identity for calls on dividend-paying stocks.
  • Use the same risk-free rate and time convention as your option chain. Mismatched compounding is a common source of apparent arbitrage.
  • Expected dividends before expiration reduce the effective stock leg through PV(Div).

Frequently asked questions

Why does this calculator offer continuous and discrete compounding?
Academic models often use continuous discounting, while many retail examples use annual discrete rates. Pick the convention that matches your inputs.
What does a non-zero parity gap mean?
It means the entered prices do not satisfy put-call parity exactly. Real markets can show small gaps because of bid-ask spreads, fees, and borrow costs.
Can I solve for the strike price?
Yes. Select Strike (K) and the tool inverts the discount factor to find the strike that satisfies parity with your call, put, and stock prices.
Are American options supported?
This tool uses the European put-call parity identity. American options may deviate when early exercise has value.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.